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Preventing noise-induced ecological shifts: stochastic sensitivity analysis and control

  • Irina Bashkirtseva
  • Lev RyashkoEmail author
Regular Article
  • 13 Downloads

Abstract

The phenomenon of the noise-induced extinction in population systems is studied. To prevent such undesirable ecological shift, we propose a new control approach based on the synthesis of the reduced stochastic sensitivity of equilibrium regime. Key points of this approach are demonstrated for the conceptual Ricker-type population model combining the Allee effect, delay, and random disturbances. This bistable population model possesses coexisting attractors corresponding to persistence and extinction regimes. To stabilize the persistence regime, feedback regulators are constructed to minimize the stochastic sensitivity of the equilibria. Cases of complete and incomplete information are reviewed and discussed.

Graphical abstract

Keywords

Statistical and Nonlinear Physics 

References

  1. 1.
    M. Scheffer, S. Carpenter, J.A. Foley, C. Folke, B. Walker, Nature 413, 591 (2001) ADSCrossRefGoogle Scholar
  2. 2.
    M. Rietkerk, S.C. Dekker, P.C. de Ruiter, J. van de Koppel, Science 305, 1926 (2004) ADSCrossRefGoogle Scholar
  3. 3.
    P.A. Stephens, W.J. Sutherland, R.P. Freckleton, Oikos 87, 185 (1999) CrossRefGoogle Scholar
  4. 4.
    B. Dennis, Oikos 96, 398 (2002) CrossRefGoogle Scholar
  5. 5.
    S.J. Schreiber, Theor. Popul. Biol. 64, 201 (2003) CrossRefGoogle Scholar
  6. 6.
    I. Bashkirtseva, L. Ryashko, Physica A 491, 28 (2018) ADSMathSciNetCrossRefGoogle Scholar
  7. 7.
    P. Turchin,Complex Population Dynamics: A Theoretical/ Empirical Synthesis (Princeton University Press, 2003) Google Scholar
  8. 8.
    A.D. Bazykin,Nonlinear Dynamics of Interacting Populations (World Scientific, 1998) Google Scholar
  9. 9.
    A. Friedman, C.-Y. Kao,Mathematical Modeling of Biological Processes (Springer, 2014) Google Scholar
  10. 10.
    F. Brauer, C. Castillo-Chavez,Mathematical Models in Population Biology and Epidemiology (Springer, 2012) Google Scholar
  11. 11.
    V.S. Anishchenko, V.V. Astakhov, A.B. Neiman, T.E. Vadivasova, L. Schimansky-Geier,Nonlinear Dynamics of Chaotic and Stochastic Systems, Tutorial and Modern Development (Springer-Verlag, Berlin, Heidelberg, 2007) Google Scholar
  12. 12.
    W. Horsthemke, R. Lefever,Noise-Induced Transitions (Springer, Berlin, 1984) Google Scholar
  13. 13.
    B. Lindner, J. Garcia-Ojalvo, A. Neiman, L. Schimansky-Geier, Phys. Rep. 392, 321 (2004) ADSCrossRefGoogle Scholar
  14. 14.
    A.S. Pikovsky, J. Kurths, Phys. Rev. Lett. 78, 775 (1997) ADSMathSciNetCrossRefGoogle Scholar
  15. 15.
    L. Gammaitoni, P. Hanggi, P. Jung, F. Marchesoni, Rev. Mod. Phys. 70, 223 (1998) ADSCrossRefGoogle Scholar
  16. 16.
    J.B. Gao, S.K. Hwang, J.M. Liu, Phys. Rev. Lett. 82, 1132 (1999) ADSCrossRefGoogle Scholar
  17. 17.
    N.V. Agudov, A.A. Dubkov, B. Spagnolo, Physica A 325, 144 (2003) ADSMathSciNetCrossRefGoogle Scholar
  18. 18.
    H.S. Wio, J.A. Revelli, M.A. Rodriguez, R.R. Deza, G.G. Izus, Eur. Phys. J. B 69, 71 (2009) ADSMathSciNetCrossRefGoogle Scholar
  19. 19.
    N.V. Agudov, A.V. Krichigin, D. Valenti, B. Spagnolo, Phys. Rev. E 81, 051123 (2010) ADSCrossRefGoogle Scholar
  20. 20.
    A.N. Pisarchik, U. Feudel, Phys. Rep. 540, 167 (2014) ADSMathSciNetCrossRefGoogle Scholar
  21. 21.
    R. Lande, Am. Nat. 142, 911 (1993) CrossRefGoogle Scholar
  22. 22.
    A. La Barbera, B. Spagnolo, Physica A 315, 114 (2002) ADSCrossRefGoogle Scholar
  23. 23.
    I. Bashkirtseva, L. Ryashko, T. Ryazanova, Eur. Phys. J. B 90, 161 (2017) ADSCrossRefGoogle Scholar
  24. 24.
    O. Chichigina, D. Valenti, B. Spagnolo, Fluctuation Noise Lett. 05, L243 (2005) CrossRefGoogle Scholar
  25. 25.
    O.A. Chichigina, A.A. Dubkov, D. Valenti, B. Spagnolo, Phys. Rev. E 84, 021134 (2011) ADSCrossRefGoogle Scholar
  26. 26.
    I. Bashkirtseva, L. Ryashko, Theor. Popul. Biol. 115, 61 (2017) CrossRefGoogle Scholar
  27. 27.
    D. Valenti, A. Fiasconaro, B. Spagnolo, Acta Phys. Pol. B 35, 1481 (2004) ADSGoogle Scholar
  28. 28.
    A. Fiasconaro, D. Valenti, B. Spagnolo, Acta Phys. Pol. B 35, 1491 (2004) ADSGoogle Scholar
  29. 29.
    D. Valenti, L. Tranchina, M. Brai, A. Caruso, C. Cosentino, B. Spagnolo, Ecol. Modell. 213, 449 (2008) CrossRefGoogle Scholar
  30. 30.
    C. Cosentino, D. Bates,Feedback Control in Systems Biology (CRC Press, 2011) Google Scholar
  31. 31.
    L. Pasotti, S. Zucca, Comput. Math. Methods Med. 2014, 369681 (2014) CrossRefGoogle Scholar
  32. 32.
    M. Porcar, J. Pereto, Integr. Biol. 8, 451 (2015) CrossRefGoogle Scholar
  33. 33.
    J.G.P. Gamarra, R.V. Sole, D. Alonso, Chaos, Solitons Fract. 12, 235 (2001) ADSCrossRefGoogle Scholar
  34. 34.
    P. Carmona, D. Franco, Nonlinear Anal. Real World Appl. 12, 3719 (2011) MathSciNetGoogle Scholar
  35. 35.
    P. Sah, J.P. Salve, S. Dey, J. Theor. Biol. 320, 113 (2013) CrossRefGoogle Scholar
  36. 36.
    S. Tung, A. Mishra, S. Dey, J. Theor. Biol. 356, 163 (2014) CrossRefGoogle Scholar
  37. 37.
    J. Segura, F.M. Hilker, D. Franco, PLoS ONE 12, e0170837 (2017) CrossRefGoogle Scholar
  38. 38.
    I. Bashkirtseva, L. Ryashko, IEEE Trans. Autom. Control 56, 2162 (2011) CrossRefGoogle Scholar
  39. 39.
    I. Bashkirtseva, G. Chen, L. Ryashko, Eur. Phys. J. B 86, 437 (2013) ADSCrossRefGoogle Scholar
  40. 40.
    I. Bashkirtseva, L. Ryashko, G. Chen, J. Franklin Inst. 354, 1658 (2017) MathSciNetCrossRefGoogle Scholar
  41. 41.
    W.E. Ricker, J. Fish. Res. Board Canada 11, 559 (1954) CrossRefGoogle Scholar
  42. 42.
    I. Bashkirtseva, L. Ryashko, Phys. Lett. A 378, 3600 (2014) ADSMathSciNetCrossRefGoogle Scholar
  43. 43.
    I. Bashkirtseva, L. Ryashko, Phys. Lett. A 381, 3203 (2017) MathSciNetCrossRefGoogle Scholar

Copyright information

© EDP Sciences / Società Italiana di Fisica / Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Theoretical and Mathematical PhysicsInstitute of Natural Science, Ural Federal UniversityEkaterinburgRussia

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